What is the solution for (d^2y)/(dx^2)+4y=1 ?

The solution for (d^2y)/(dx^2)+4y=1 is y=c_{1}cos(2x)+c_{2}sin(2x)+1/4

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(d^2y)/(dx^2)+4y=1

\frac{d ^{2} y}{d x ^{2}} + 4 y = 1

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{1}{4}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 4 y = 1

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{1}{4}

y = c_{1} cos (2 x) + c_{2} sin (2 x) + \frac{1}{4}

y^{^{''}} + 9 y = 2 sin (x)

y^{^{''}} + 14 y^{^{'}} + 49 y = e^{- 7 t} ln (t)

y^{^{''}} + y^{^{'}} + y = k (e^{- t} + sin (2 t))

y^{^{''}} - 5 y^{^{'}} + 6 y = cos (t) - t e^{t}

y^{^{''}} - y^{^{'}} - 12 y = 5 e^{2 x} - 4

What is the solution for (d^2y)/(dx^2)+4y=1 ?
The solution for (d^2y)/(dx^2)+4y=1 is y=c_{1}cos(2x)+c_{2}sin(2x)+1/4